Focused ion beam (FIB) and scanning electron microscopy (SEM) are used to reversibly switch improper ferroelectric domains in the hexagonal manganite ErMnO$_3$. Surface charging is achieved by local ion (positive charging) and electron (positive and negative charging) irradiation, which allows controlled polarization switching without the need for electrical contacts. Polarization cycling reveals that the domain walls tend to return to the equilibrium configuration obtained in the as-grown state. The electric field response of sub-surface domains is studied by FIB cross-sectioning, revealing the 3D switching behavior. The results clarify how the polarization reversal in hexagonal manganites progresses at the level of domains, resolving both domain wall movements and the nucleation and growth of new domains. Our FIB-SEM based switching approach is applicable to all ferroelectrics where a sufficiently large electric field can be built up via surface charging, facilitating contact-free high-resolution studies of the domain and domain wall response to electric fields in 3D.
We performed first principles calculations for epitaxially strained orthorhombic CaTiO$_3$. The computational results reveal the existence of a metastable ferroelectric phase at compressive strain with unexpected in-plane polarization. Symmetry analysis indicates that two distortion modes at the X point combine to induce the polarization, leading to characterization as a hybrid improper ferroelectric. Our work demonstrates a mechanism for improper ferroelectricity in simple perovskites without the need for symmetry lowering by layering or cation ordering.
Integration of ferroelectric materials into novel technological applications requires low coercive field materials, and consequently, design strategies to reduce the ferroelectric switching barriers. In this first principles study, we show that biaxial strain, which has a strong effect on the ferroelectric ground states, can also be used to tune the switching barrier of hybrid improper ferroelectric Ruddlesden-Popper oxides. We identify the region of the strain -- tolerance factor phase diagram where this intrinsic barrier is suppressed, and show that it can be explained in relation to strain …
We study the ferroelectric stability and surface structural properties of an oxygen-terminated hexagonal YMnO$_3$ ultra-thin film using density functional theory. Under an open circuit boundary condition, the ferroelectric state with the spontaneous polarization normal to the (0001) surface, is found to be metastable in a single domain state despite the presence of a depolarizing field. We establish a connection between the result and the role of improper ferroelectric transition. Our results imply that improper ferroelectric ultrathin films can have rather unique properties that are distincti…
In this contribution to the special issue on magnetoelectrics and their applications, we focus on some single phase multiferroics theoretically predicted and/or experimentally discovered by the authors in recent years. In these materials, iron is the common core element. However, these materials are conceptually different from the mostly-studied BiFeO$_3$, since their ferroelectricity is improper. Our reviewed materials are not simply repeating one magnetoelectric mechanism, but cover multiple branches of improper ferroelectricity, including the magnetism-driven ferroelectrics, geometric ferro…
First-principles calculations are presented for the layered perovskite Ca$_3$Mn$_2$O$_7$. The results reveal a rich set of coupled structural, magnetic and polar domains in which oxygen octahedron rotations induce ferroelectricity, magnetoelectricity and weak-ferromagnetism. The key point is that the rotation distortion is a combination of two non-polar modes with different symmetries. We use the term "hybrid" improper ferroelectricity to describe this phenomenon and discuss how control over magnetism is achieved through these functional antiferrodistortive octahedron rotations.
Improper ferroelectrics are described by two order parameters: a primary one, driving a transition to long-range distortive, magnetic or otherwise non-electric order, and the electric polarization, which is induced by the primary order parameter as a secondary, complementary effect. Using low-temperature scanning probe microscopy, we show that improper ferroelectric domains in YMnO$_3$ can be locally switched by electric field poling. However, subsequent temperature changes restore the as-grown domain structure as determined by the primary lattice distortion. The backswitching is explained by …
Cornell University（康奈尔大学）；University of Nebraska, Lincoln（内布拉斯加大学林肯分校）；Leibniz-Institut für Kristallzüchtung（莱布尼茨晶体生长研究所）；Pacific Northwest National Laboratory（太平洋西北国家实验室）；The Pennsylvania State University（宾夕法尼亚州立大学）；University of California, Berkeley（加州大学伯克利分校）；Rice University（莱斯大学）；Kavli Institute at Cornell for Nanoscale Science（康奈尔卡弗里纳米科学研究所）；Princeton University（普林斯顿大学）
Li et al. (Science Advances, 29 January, p. eabe3068) claim the discovery of two improper ferroelectrics, dabcoHClO4 and dabcoHBF4 (dabco = 1,4-diazabicyclo[2.2.2]octane), and that these materials exhibit superior pyroelectric figures of merit. This information is misleading due to the fundamental methodological errors and false conclusions, not to mention that these ferroelectrics were reported over 20 years ago. They are proper ferroelectrics, for which the spontaneous polarization is the macroscopic order parameter. We show that the useful pyroelectric coefficients of these materials are ab…
The successful theoretical prediction and experimental demonstration of hybrid improper ferroelectricity (HIF) provides a new pathway to couple octahedral rotations, ferroelectricity, and magnetism in complex materials. To enable technological applications, a HIF with a small coercive field is desirable. We successfully grow Sr3Sn2O7 single crystals, and discover that they exhibit the smallest electric coercive field at room temperature among all known HIFs. Furthermore, we demonstate that a small external stress can repeatedly erase and re-generate ferroelastic domains. In addition, using in-…
Gadolinium molybdate is a classical example of an improper ferroelectric and ferroelastic material. It is established that the spontaneous polarization arises as a secondary effect, induced by a structural instability in the paraelectric phase, which leads to a unit cell doubling and the formation of a polar axis. However, previous X-ray diffraction studies on gadolinium molybdate have been restricted by the limited ability to include the entire 2θ range in the analysis, and thus, at atomic scale, much remains to be explored. By applying temperature dependent X-ray diffraction, we observe the …
Charged polar interfaces such as charged ferroelectric domain walls or heterostructured interfaces of ZnO/(Zn,Mg)O and LaAlO3/SrTiO3, across which the normal component of electric polarization changes suddenly, can host large two-dimensional conduction. Charged ferroelectric walls, which are energetically unfavorable in general, were found to be mysteriously abundant in hybrid improper ferroelectric (Ca,Sr)3Ti2O7 crystals. From the exploration of antiphase boundaries in bilayer-perovskites, we discover that each of four polarization-direction states is degenerated with two antiphase domains, a…
We report on multiple fundamental qualitative improvements in the growth of improper ferroelectric hexagonal YMnO$_3$ (YMO) thin films and heterostructures by pulsed laser deposition (PLD). By a combination of pre-growth substrate annealing and low-energy-fluence PLD, we obtain a two-dimensional growth mode of the YMO films on yttria-stabilized zirconia (YSZ) with ultralow roughness and devoid of misoriented nanocrystalline inclusions. By inserting a sacrificial manganite layer capped with conducting indium-tin oxide between the substrate and the final film, the latter is grown in a fully latt…
Ferroelectric domain walls are attracting broad attention as atomic-scale switches, diodes and mobile wires for next-generation nanoelectronics. Charged domain walls in improper ferroelectrics are particularly interesting as they offer multifunctional properties and an inherent stability not found in proper ferroelectrics. Here we study the energetics and structure of charged walls in improper ferroelectric YMnO$_3$, InMnO$_3$ and YGaO$_3$ by first principles calculations and phenomenological modeling. Positively and negatively charged walls are asymmetric in terms of local structure and width…
Hybrid improper ferroelectrics (HIFs) have been intensely studied over the last few years to gain understanding of their temperature induced phase transitions and ferroelectric switching pathways. Here we report a switching from first- to second-order phase transition pathway for topical HIFs $Ca_{3-x}Sr_xTi_2O_7$, which is driven by the differing entropies of the phases that we identify as being associated with the dynamic motion of octahedral tilts and rotations. A greater understanding of the transition pathways in this class of layered perovskites, which host many physical properties that …
The presence of a switchable spontaneous electric polarization makes ferroelectrics ideal candidates for the use in many applications such as memory and sensors devices. Since known ferroelectrics are rather limited, finding new ferroelectric (FE) materials has become a flourishing field. One promising route is to design the so-called hybrid improper ferroelectricity. However, the previous approach based on the Landau theory is not easily adopted to the systems that are unrelated to the Pbnm perovskite structure. To this end, we develop a general design rule that is applicable to any systems. …
We study the interplay of structural and polar distortions in hexagonal YMnO3 and short-period PbTiO3/SrTiO3 superlattices by means of first-principles calculations at constrained electric displacement field D. We find that in YMnO3 the tilts of the oxygen polyhedra produce a robustly polar ground state, which persists at any choice of the electrical boundary conditions. Conversely, in PTO/STO the antiferrodistortive instabilities alone do not break inversion symmetry, and open-circuit bundary conditions restore a non-polar state. We suggest that this qualitative difference naturally provides …
The improper ferroelectricity in YMnO$_3$ and other related multiferroic hexagonal manganites are known to cause topologically protected ferroelectric domains that give rise to rich and diverse physical phenomena. The local structure and structural coherence across the ferroelectric transition, however, were previously not well understood. Here we reveal the evolution of the local structure with temperature in YMnO$_3$ using neutron total scattering techniques, and interpret them with the help of first-principles calculations. The results show that, at room temperature, the local and average s…
We report the dielectric properties of improper ferroelectric h-ErMnO$_3$. From the bulk characterisation we observe a temperature and frequency range with two distinct relaxation-like features, leading to high and even 'colossal' values for the dielectric permittivity. One feature trivially originates from the formation of a Schottky barrier at the electrode-sample interface, whereas the second one relates to an internal barrier layer capacitance (BLC). The calculated volume fraction of the internal BLC (of 8 %) is in good agreement with the observed volume fraction of insulating domain walls…
Charged domain walls and boundaries in ferroelectric materials display distinct phenomena, such as an increased conductivity due to the accumulation of bound charges. Here, we report the electron microscopy observations of atomic-scale arrangements at charged domain boundaries in the hybrid improper ferroelectric Ca$_{2.46}$Sr$_{0.54}$Ti$_2$O$_7$. Like in the prototype improper ferroelectric YMnO$_3$, we find that charged domain boundaries in Ca$_{2.46}$Sr$_{0.54}$Ti$_2$O$_7$ correspond to out-of-phase boundaries, which separate adjacent domains with a fractional translational shift of the uni…
In hybrid improper ferroelectric systems, polarization arises from the onset of successive nonpolar lattice modes. In this work, measurements and modeling were performed to determine the spatial symmetries of the phases involved in the transitions to these modes. Structural and optical measurements reveal that the tilt and rotation distortions of the MnO6 or TiO6 polyhedra relative to the high symmetry phases driving ferroelectricity in the hybrid improper Ca3X2O7 system (X=Mn and Ti) condense at different temperatures. The tilt angle vanishes abruptly at T$_T$ ~ 400 K for Ca3Mn2O7 (and contin…
Standing on successful first principles predictions for new functional ferroelectric materials, a number of new ferroelectrics have been experimentally discovered. Utilizing trilinear coupling of two types of octahedron rotations, hybrid improper ferroelectricity has been theoretically predicted in ordered perovskites and the Ruddlesden-Popper compounds (Ca$_{3}$Ti$_{2}$O$_{7}$, Ca$_{3}$Mn$_{2}$O$_{7}$, and (Ca/Sr/Ba)$_{3}$(Sn/Zr/Ge)$_{2}$O$_{7}$). However, the ferroelectricity of these compounds has never been experimentally confirmed and even their polar nature has been under debate. Here we…
Ca$_3$Ti$_2$O$_7$ is an experimentally confirmed hybrid improper ferroelectric material, in which the electric polarization is induced by a combination of the coherent TiO$_6$ octahedral rotation and tilting. In this work, we investigate the tuning of ferroelectricity of Ca$_3$Ti$_2$O$_7$ using iso-valent substitutions on Ca-sites. Due to the size mismatch, larger/smaller alkaline earths prefer $A$'/$A$ sites respectively, allowing the possibility for site-selective substitutions. Without extra carriers, such site-selected iso-valent substitutions can significantly tune the TiO$_6$ octahedral …
Ferroic materials are well known to exhibit heterogeneity in the form of domain walls. Understanding the properties of these boundaries is crucial for controlling functionality with external stimuli and for realizing their potential for ultra-low power memory and logic devices as well as novel computing architectures. In this work, we employ synchrotron-based near-field infrared nano-spectroscopy to reveal the vibrational properties of ferroelastic (90$^\circ$ ferroelectric) domain walls in the hybrid improper ferroelectric Ca$_3$Ti$_2$O$_7$. By locally mapping the Ti-O stretching and Ti-O-Ti …
The temperature-dependent phase transitions in Ruddlesden-Popper oxides with perovskite bilayers have been under increased scrutiny in recent years due to the so-called hybrid improper ferroelectricity that some chemical compositions exhibit. However, little is currently understood about the hydrostatic pressure dependence of these phase transitions. Herein we present the results of a high-pressure powder synchrotron X-ray diffraction experiment and $ab~initio$ calculations on the bilayered Ruddlesden-Popper phases Ca$_{3}$Mn$_{2}$O$_{7}$ and Ca$_{3}$Ti$_{2}$O$_{7}$. In both compounds we obser…
We have carried out a first-principles theoretical study of the magnetically induced polarization in orthorhombic TbMnO3, a prototypical material in which a cycloidal spin structure generates an electric polarization via the spin-orbit interaction. We compute both the electronic and the lattice-mediated contributions to the polarization and find that the latter is strongly dominant. We analyze the spin-orbit induced forces and lattice displacements from both atomic and mode-decomposition viewpoints, and show that a simple model based on nearest Mn--Mn neighbor Dzyaloshinskii-Moriya interaction…
Two-dimensional (2D) hybrid organic-inorganic perovskites (HOIPs) are introducing new directions in the 2D materials landscape. The coexistence of ferroelectricity and spin-orbit interactions play a key role in their optoelectronic properties. We perform a detailed study on a recently synthesized ferroelectric 2D-HOIP, (AMP)PbI$_4$ (AMP = 4-aminomethyl-piperidinium). The calculated polarization and Rashba parameter are in excellent agreement with experimental values. We report a striking new effect, i.e., an extraordinarily large Rashba anisotropy that is tunable by ferroelectric polarization:…
Using first principles calculations, we study the microscopic origin of ferroelectricity (FE) induced by magnetic order in the orthorhombic HoMnO3. We obtain the largest ferroelectric polarization observed in the whole class of improper magnetic ferroelectrics to date. We find that the two proposed mechanisms for FE in multiferroics, lattice- and electronic-based, are simultaneously active in this compound: a large portion of the ferroelectric polarization arises due to quantum-mechanical effects of electron orbital polarization, in addition to the conventional polar atomic displacements. An i…
We demonstrate that electromagnons can be used to directly probe the nature of a phase transition between magnetically ordered phases in an improper ferroelectric. The antiferromagnetic/paraelectric to antiferromagnetic/ferroelectric phase transition in Cu$_{1-x}$Zn$_{x}$O ($x=0, 0.05$) alloys was tracked via the electromagnon response using terahertz time-domain spectroscopy, on heating and cooling through the phase transition. The transition was found to exhibit thermal hysteresis, confirming its first-order nature, and to broaden under the influence of spin-disorder upon Zn substitution. Th…
Electronic and structural phenomena at the twin domain wall-surface junctions in the ferroelastic materials are analyzed. Carriers accumulation caused by the strain-induced band structure changes originated via the deformation potential mechanism, structural order parameter gradient, rotostriction and flexoelectric coupling is explored. Approximate analytical results show that inhomogeneous elastic strains, which exist in the vicinity of the twin walls - surface junctions due to the rotostriction coupling, decrease the local band gap via the deformation potential and flexoelectric coupling mec…
The noncollinear cycloidal magnetic order breaks the inversion symmetry in CaMn$_{7}$O$_{12}$, generating one of the largest spin-orbit driven ferroelectric polarizations measured to date. In this Letter, the microscopic origin of the polarization, including its direction, charge density redistribution, magnetic exchange interactions, and its coupling to the spin helicity, is explored via first principles calculations. The Berry phase computed polarization exhibits almost pure electronic behavior, as the Mn displacements are negligible, $\approx$~0.7~m\textrmÅ. The polarization magnitude and d…
We propose the Landau model for lock-in phase transitions in uniaxially modulated improper ferroelectric incommensurate-commensurate systems of class I. It includes Umklapp terms of third and fourth order and secondary order parameter representing the local polarization. The corresponding phase diagram has the structure of harmless staircase, with the allowed wave numbers obeying the Farey tree algorithm. Among the stable commensurate phases only those with periods equal to odd number of lattice constants have finite macroscopic polarizations. These results are in excellent agreement with expe…
Recent interests towards novel functionalities arising at domain walls of ferroic materials naturally call for a microscopic understanding. To this end, first-principles calculations have been performed in order to provide solid evidence of ferroelectricity in the twin walls of nonpolar CaTiO3 and magnetic CaMnO3. We show that ferroelectricity arises from rotation/tilting octahedral distortions --- cooperatively acting at the twin wall in both considered systems --- rather than from a proper secondary ferroelectric instability, as often believed. Our results are in excellent agreement with exp…
It is of great interest to design and make materials in which ferroelectric polarisation is coupled to other order parameters such as lattice, magnetic and electronic instabilities. Such materials will be invaluable in next-generation data storage devices. Recently, remarkable progress has been made in understanding improper ferroelectric coupling mechanisms that arise from lattice and magnetic instabilities. However, although theoretically predicted, a compact lattice coupling between electronic and ferroelectric (polar) instabilities has yet to be realised. Here we report detailed crystallog…
The charged domain walls in ferroelectric materials exhibit intriguing physical properties. We examine herein the charged-domain-wall structures in Ca$_{3-x}$Sr$_x$Ti$_2$O$_7$ using transmission electron microscopy. When viewed along the [001] axis, the wavy charged domain walls are observed over a wide range ($>$5 $μ$m). In contrast, short charged-domain-wall fragments (from 10 to 200 nm long) occur because they are intercepted and truncated by the conventional 180$^°$ domain walls. These results reveal the unusual charged domain structures in Ca$_{3-x}$Sr$_x$Ti$_2$O$_7$ and will be useful fo…
Cu3Nb2O8 is an unusual multiferroic compound that undergoes a series of magnetic ordering at low temperatures. Concurrent development of electric polarization has been reported at TN1 ~25 K corresponding to a non-collinear helicoidal ordering (Phys. Rev. Lett. 107, 137205 (2011)). But questions remain on the microscopic origin of such phenomena. In this communication, we report a detailed study of induced polar ordering in Cu3Nb2O8 by performing polarization, magnetization, dielectric constant and heat capacity measurements over a broad range of temperature and magnetic field. The dielectric c…
Ferroelectric domain walls represent multifunctional 2D-elements with great potential for novel device paradigms at the nanoscale. Improper ferroelectrics display particularly promising types of domain walls, which, due to their unique robustness, are the ideal template for imposing specific electronic behavior. Chemical doping, for instance, induces p- or n-type characteristics and electric fields reversibly switch between resistive and conductive domain-wall states. Here, we demonstrate diode-like conversion of alternating-current (AC) into direct-current (DC) output based on neutral 180$^{\…
Transition metal oxides hold great potential for the development of new device paradigms because of the field-tunable functionalities driven by their strong electronic correlations, combined with their earth abundance and environmental friendliness. Recently, the interfaces between transition-metal oxides have revealed striking phenomena such as insulator-metal transitions, magnetism, magnetoresistance, and superconductivity. Such oxide interfaces are usually produced by sophisticated layer-by-layer growth techniques, which can yield high quality, epitaxial interfaces with almost monolayer con…
Doping ferroelectrics with carriers is often detrimental to polarization. This makes the design and discovery of metals that undergo a ferroelectric-like transition challenging. In this letter, we show from first principles that the oxygen octahedral rotations in perovskites are often enhanced by electron doping, and this can be used as a means to strengthen the structural polarization in certain hybrid-improper ferroelectrics -- compounds in which the polarization is not stabilized by the long range Coulomb interactions but is instead induced by a trilinear coupling to octahedral rotations. W…
We present a detailed study of the structural, electronic, magnetic and ferroelectric properties of prototypical \textit{proper} and \textit{improper} multiferroic (MF) systems such as BiFeO$_{3}$ and orthorhombic HoMnO$_{3}$, respectively, within density functional theory (DFT) and using the Heyd-Scuseria-Ernzerhof hybrid functional (HSE). By comparing our results with available experimental data as well as with state-of-the-art GW calculations, we show that the HSE formalism is able to account well for the relevant properties of these compounds and it emerges as an accurate tool for predicti…
Using a joint approach of density functional theory and model calculations, we demonstrate that a prototypical charge ordered half-doped manganite, La$_{1/2}$Ca$_{1/2}$MnO$_3$ is multiferroic. The combination of a peculiar charge-orbital ordering and a tendency to form spin dimers breaks inversion symmetry, leads to a ferroelectric ground-state with a polarization up to several $μC/cm^2$. The presence of improper ferroelectricity does not depend on hotly debated structural details of this material: in the Zener-polaron structure we find a similar dramatic ferroelectric response with a large po…
Recent experimental and theoretical work has shown that the double perovskite NaLaMnWO$_6$ exhibits antiferromagnetic ordering owing to the Mn $d$ states, and computational studies further predict it to exhibit a spontaneous electric polarization due to an improper mechanism for ferroelectricity [King \textit{et al., Phys.\ Rev.\ B}, 2009, \textbf{79}, 224428; Fukushima \textit{et al., Phys.\ Chem.\ Chem.\ Phys.}, 2011, \textbf{13}, 12186], which make it a candidate multiferroic material. Using first-principles density functional calculations, we investigate nine isostructural and isovalent $A…
Hexagonal RMnO3 manganites are improper ferroelectrics in which the electric polarization is a by-product of the tripling of the unit cell. In YMnO3, there is a second transition at ~ 920K whose nature remains unexplained. We argue that this transition can be seen as a sort of hidden order in which a residual symmetry displayed by the trimerization order parameter is spontaneously broken. This additional order gives rise to twelve structural domains instead of six, and structural domain boundaries that can be either ferroelectric or non-ferroelectric domain walls.
Two-dimensional (2D) ferroelectricity has attracted extensive attention since its discovery in the monolayers of van der Waals materials. Here we show that 2D ferroelectricity induced by octahedral rotation distortion is widely present in the perovskite bilayer system through first-principles calculations. The perovskite tolerance factor plays a crucial role in the lattice dynamics and ground-state structure of the perovskite monolayers and bilayers, thus providing an important indicator for screening this hybrid improper ferroelectricity. Generally, the ferroelectric switching via an orthorho…
Hybrid improper ferroelectricity, where an electrical polarization can be induced via a trilinear coupling to two non-polar structural distortions of different symmetry, has recently been experimentally demonstrated for the first time in the $n$=2 Ruddlesden-Popper compound Ca$_3$Ti$_2$O$_7$. In this paper we use group theoretic methods and first-principles calculations to identify possible ferroelectric switching pathways in Ca$_3$Ti$_2$O$_7$. We identify low-energy paths that reverse the polarization direction by switching via an orthorhombic twin domain, or via an antipolar structure. We al…
We report $α$-Cu$_2$V$_2$O$_7$ to be an improper multiferroic with the simultaneous development of electric polarization and magnetization below $T_C$ = 35 K. The observed spontaneous polarization of magnitude 0.55 $μ$Ccm$^{-2}$ is highest among the copper based improper multiferroic materials. Our study demonstrates sizable amount of magneto-electric coupling below $T_C$ even with a low magnetic field. The theoretical calculations based on density functional theory (DFT) indicate magnetism in $α$-Cu$_2$V$_2$O$_7$ is a consequence of {\em ferro-orbital} ordering driven by polar lattice distort…
The research on topological phenomena in ferroelectric materials has revolutionized the way we understand polar order. Intriguing examples are polar skyrmions, vortex/anti-vortex structures and ferroelectric incommensurabilties, which promote emergent physical properties ranging from electric-field-controllable chirality to negative capacitance effects. Here, we study the impact of topologically protected vortices on the domain formation in improper ferroelectric ErMnO3 polycrystals, demonstrating inverted domain scaling behavior compared to classical ferroelectrics. We observe that as the gra…
